Newcomb's Problem

[Erik Mesoy]

"The following may well be the most controversial dilemma in the history of decision theory."

A superintelligence from another galaxy, whom we shall call Omega, comes to Earth and sets about playing a strange little game. In this game, Omega selects a human being, sets down two boxes in front of them, and flies away.

Box A is transparent and contains a thousand dollars.
Box B is opaque, and contains either a million dollars, or nothing.

You can take both boxes, or take only box B.

And the twist is that Omega has put a million dollars in box B iff Omega has predicted that you will take only box B.

Omega has been correct on each of 100 observed occasions so far - everyone who took both boxes has found box B empty and received only a thousand dollars; everyone who took only box B has found B containing a million dollars. (We assume that box A vanishes in a puff of smoke if you take only box B; no one else can take box A afterward.)

Before you make your choice, Omega has flown off and moved on to its next game. Box B is already empty or already full.

Omega drops two boxes on the ground in front of you and flies off.

Do you take both boxes, or only box B?

http://pastie.caboo.se/195189.txt

Assume that you're playing the game in the above situation and that the rules have been explained to you, then vote in the poll.

The usual positions in the argument are as follows.

TWO-BOXER:

Spoiler :

Why you should pick both boxes:

The key here is that Omega (the alien) has already put the money is the boxes before you decide whether to take both boxes or just box b. In other words, your decision cannot affect what is in the boxes, because the money was put there IN THE PAST.

That means there are two possible scenarios: either there is $1,000,000 in box b, or there is not. Remember that your choice of box does not determine which of these scenarios actually exists... that is arbitrarily chosen by the alien. Now, for either scenario, taking both boxes will get you whatever is in box b AND $1,000 extra dollars. That means that regardless of what is in the two boxes, taking both will ALWAYS get you $1,000 more than if you had just taken box b. It is stupid, then, not to take both... unless you don't like money!

Erik will doubtless argue that he will be "$900,000 richer than you," but while this may be true, you are $1,000 richer than you would have been if you had taken box b, so his good fortune has no bearing on how much money YOU have. The alien having been right 100% of the time before is equally irrelevant: the implication is supposed to be that he was automatically right this time, but that is untrue. The alien made his decision, and you then made yours; the two were unrelated, and all you did was maximize your profits.

ONE-BOXER:

Spoiler :

Knowing that Omega has a 100/100 correctness rate so far, I assign at least a 99% probability that he'll be correct in predicting what I pick. So my expectation from picking both boxes is (0.99*1000 + 0.01*1000) + (0.99*0 + 0.01 * 1000000) = $11000, while my expectation from picking box B is (0.99 * 1000000 + 0.01*0) = $990000. Thus I should pick box B.

Or to make it simpler, anyone who agrees with my point of view should expect a million dollars, and anyone who disagrees should expect a thousand dollars. By any sane metric of reasonable thought, mine is preferable.

One-boxers are usually confident that their opinion is correct and that picking two boxes is silly. Two-boxers are usually confident that their opinion is correct and that picking one box is silly. Nonetheless, people tend to be about evenly split on the issue.

Let the arguing begin. Which do you pick, and why?

Addendum: "iff" in the starting quote means "if and only if".

 

[amadeus]

B.

A thousand dollars isn't enough to interest me; I'm a high stakes gambler.

 

[Defiant47]

This is still tricky

 

[Virote_Considon]

Box B! Box B!

Then I could finally feel like a million dollars!

And If I don't get the million, then I have lost nothing.

1234567890

 

[philippe]

1234567890

I'm with virote, then again I misclicked
<@philippe> goddamnit
<@philippe> I misvoted
<+Psweet> how do you misvote?
* dutchfire rants about the stupidity of belgians
<+Psweet> the options are even spelled out phonetically!

 

[amadeus]

Looks a little heavy in favor of BEEEES at the moment. Will it level off?

 

[nihilistic]

Both. If I end up with 1000 there is an understanding. If I end up with 1001000 I would have screwed the pathetic 'super-intelligent' being.

Unless the 'super-intelligent' being has published probabilities of false negatives and it favored choosing the other.

 

[Defiant47]

I guess this is simply a matter of how much do we trust its predictions, given 100/100 data.

 

[Kozmos]

Well if it states EVERYONE who has taken only box B has found a million dollars, I dont quite see the dilemma here.

 

[Phlegmak]

B.

$1000 extra to me isn't much.

$1M extra to me is a lot.

The deciding factor was that Omega was 100% correct in all his predictions in where he'd put the money. It's 99% probable he'd be right with me, and so I'll just take box B.

 

[Perfection]

Here's the Perfection way.

1. I ask Omega if the device is optimized for hits to misses ratio. If he disagrees, I go box B, otherwise I continue
2. I wait until the boxes are down and contents settled
3. I use a source of quantum randomness that produces a number randomly from a large field
4. I pick a subfield of the numbers that has a slightly less then 50% of coming up
5. If a number in that subfield comes up I take both, if not I take box b.

The result is a slightly more then 50% chance of getting a million dollars, a slightly less than 50% chance of getting a million one thousand dollars and the glory of having outsmarted Omega.

 

[Erik Mesoy]

Here's the Perfection way.

1. I ask the aliens
[...]

The alien has flown away after dropping the boxes. You don't get to ask it questions.

 

[Catharsis]

Both. Here's the reasoning:

If you take both boxes, then you have $1000 and two boxes. So you can buy $1000 worth of stuff, and two boxes is an adequate amount of space to hold $1000 worth of stuff.

If you take box B, then you have either $0, in which case you have a box but nothing to put in it (waste of a box), or $1000000, which means you can buy $1000000 worth of stuff, but you only have one box in which to put it - and as we've seen, one box can only be reasonably expected to hold $500 worth of stuff, so $999500 worth of your stuff will have no box and will therefore get wet in the rain.

QED.

 

[Perfection]

The alien has flown away after dropping the boxes. You don't get to ask it questions.

In that case I make the assumption.

 

[nivi]

Box B, of course. I mean really, a 100/100 chance is good enough for me, the extra (or only) 1000 isn't worth it enough to make me risk 1m$.

 

[dutchfire]

Both. Here's the reasoning:

If you take both boxes, then you have $1000 and two boxes. So you can buy $1000 worth of stuff, and two boxes is an adequate amount of space to hold $1000 worth of stuff.

If you take box B, then you have either $0, in which case you have a box but nothing to put in it (waste of a box), or $1000000, which means you can buy $1000000 worth of stuff, but you only have one box in which to put it - and as we've seen, one box can only be reasonably expected to hold $500 worth of stuff, so $999500 worth of your stuff will have no box and will therefore get wet in the rain.

QED.

Move away from rainy England and you remove that problem.

 

[dcbandicoot]

Both. Regardless of what box I choose, there's $0 or $1m in the box. So why not take the free $1000?

I don't understand why everyone believes 100 correct out of 100 is relevant, or why choosing just the opaque box is the right choice. The money's THERE or it's NOT regardless of what you choose, it's NOT guaranteed if you just take box B.

 

[Perfection]

You know, something that hasn't been mentioned here is how much the boxes are worth. I mean, boxes made by superintelligent aliens could be worth a lot of scratch,

 

[Catharsis]

Move away from rainy England and you remove that problem.

And how, pray tell, would I move $1000000 worth of stuff out of England with only one box?

 

[Perfection]

You could buy more boxes!